## Mathematics and Computer Science

#### Event Title

#### Document Type

Oral Presentation

#### Location

Indianapolis, IN

#### Subject Area

Physics, Mathematics & Computer Science

#### Start Date

10-4-2015 10:15 AM

#### End Date

10-4-2015 10:45 AM

#### Sponsor

Stacy Hoehn (Franklin College)

#### Description

The 15 Puzzle is a 4x4 puzzle with 15 pieces numbered 1 through 15 and one blank space. To solve the puzzle, one must slide one piece at a time until the pieces are in numerical order and the blank space is in the 16th spot. Topspin is a puzzle consisting of 20 pieces numbered 1 through 20 that form an oval track. To solve the puzzle, one must manipulate the order of the numbers by flipping the turnstile holding 4 pieces and by shifting the numbers around the track until the pieces are in numerical order. I will be discussing the mathematics behind the 15 Puzzle and TopSpin, including why these puzzles work and how to know up front if the puzzles are solvable. I will also include algorithms to solve the puzzles and explain how these algorithms relate to the symmetric group from Modern Algebra.

Modern Algebra of The 15 Puzzle and Topspin

Indianapolis, IN

The 15 Puzzle is a 4x4 puzzle with 15 pieces numbered 1 through 15 and one blank space. To solve the puzzle, one must slide one piece at a time until the pieces are in numerical order and the blank space is in the 16th spot. Topspin is a puzzle consisting of 20 pieces numbered 1 through 20 that form an oval track. To solve the puzzle, one must manipulate the order of the numbers by flipping the turnstile holding 4 pieces and by shifting the numbers around the track until the pieces are in numerical order. I will be discussing the mathematics behind the 15 Puzzle and TopSpin, including why these puzzles work and how to know up front if the puzzles are solvable. I will also include algorithms to solve the puzzles and explain how these algorithms relate to the symmetric group from Modern Algebra.